Practice-Using the Discriminant 1. Learn how to find the discriminant and number of solutions for quadratic equations.The discriminant shows whether the values x x are all real roots or some are complex roots with i=√−1 i = − 1 . So I calculated the discriminant −3−4i and now I proceed to calculate roots of such number to plug them into the formula for "normal" roots. There are 3 possible cases (see the image below as well). 04a. Quadratics – the quadratic formula and the discriminant - Free download as PDF File (. Completing the square means taking a quadratic function from its standard form that has two x-variables down to its vertex form, which only has one x- variable. The Maths Prof: The Discriminant (b²-4ac).